MinT - Best Known (80, 80+42, s)-Nets in Base 5

Best Known (80, 80+42, s)-Nets in Base 5

(80, 80+42, 296)-Net over F₅ — Constructive and digital

Digital (80, 122, 296)-net over F₅, using

trace code for nets [i] based on digital (19, 61, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(80, 80+42, 488)-Net over F₅ — Digital

Digital (80, 122, 488)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+42, 24937)-Net in Base 5 — Upper bound on s

There is no (80, 122, 24938)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 18 818462 962106 396401 157553 024544 890369 315927 746711 385602 713491 922028 071041 464359 964585 > 5¹²² [i]